how do i rig and animate a tree in blender without using "Sapling" addon ?
Shift A: add an Armature (new bone). Then, in edit mode E extrude all the bones you need and move their junctions following the shape of the tree (in the properties panel you can enable the "X rays" view to see your bones also if they are inside the tree).
If you want precision bones placement: select an edge loop, Shift S "Cursor to selected", select the bones junction, Shift S "selection to cursor".

Then in object mode select the tree, shift select the armature, Ctrl P parent "with automatic weights".

Select the armature, switch to pose mode and animate.
In the modifier stack set the subsurf modifier after the armature modifier.